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angle of view of a line segment

Let P⁢QPQPQ be a line segment and AAA a point not belonging to P⁢QPQPQ. Let the magnitude of the angleP⁢A⁢QPAQPAQ be αα\alpha. One says that the line segment P⁢QPQPQis seen from the point AAA in an angle of αα\alpha; one may also speak of the angle of view of P⁢QPQPQ.

The locus of the points from which a given line segment P⁢QPQPQ is seen in an angle of αα\alpha (with 0<α<180∘0αsuperscript1800<\alpha<180^{\circ}) consists of two congruentcirculararcs having the line segment as the common chord and containing the circumferential angles equal to αα\alpha.

Especially, the locus of the points from which the line segment is seen in an angle of 90∘superscript9090^{\circ} is the circle having the line segment as its diameter.

PPPQQQαα\alphaαα\alpha..

Note. The explementary arcs of the above mentioned two arcs form the locus of the points from which the segmentP⁢QPQPQ is seen in the angle 180∘-αsuperscript180α180^{\circ}\!-\!\alpha.